Thanks to all who've commented so far.
@josh.. No, you're right.. it shouldn't look like the water was moving.
It boils down to one simple problem: I wanted a bog but designed a swamp.
That's the reason why the displacement (those aren't waves) looks like waves.
The water in the previous version was quite calm but I tried to optimize the image, removed some shaders and after 62 hours it turned out the displacement looked like waves. This wasn't intended but the motivation to do any further work is quite small when you have to wait three days for the render to complete.
Unfortunately, just removing displacement really made things worse.. now it looks like a mirror.